# The adaptive EM schemes for McKean-Vlasov SDEs with common noise in finite and infinite horizons

## TL;DR

This paper develops adaptive Euler-Maruyama schemes for McKean-Vlasov SDEs with common noise, establishing convergence rates under superlinear growth conditions and demonstrating their effectiveness through numerical examples.

## Contribution

It introduces adaptive EM schemes for McKean-Vlasov SDEs with common noise, providing convergence analysis under superlinear growth conditions.

## Key findings

- Established $L^p$ convergence rates in finite and infinite horizons.
- Demonstrated the schemes' effectiveness through numerical examples.

## Abstract

This paper is dedicated to investigating the adaptive Euler-Maruyama (EM) schemes for the approximation of McKean-Vlasov stochastic differential equations (SDEs) with common noise. When the drift and diffusion coefficients both satisfy the superlinear growth conditions, the $L^p$ convergence rates in finite and infinite horizons are revealed, which reacts to the particle number and step size. Subsequently, there is an illustration of the theory results by means of two numerical examples.